Problem: Solve for $x$ and $y$ using substitution. ${-5x-2y = 5}$ ${y = x-6}$
Since $y$ has already been solved for, substitute $x-6$ for $y$ in the first equation. ${-5x - 2}{(x-6)}{= 5}$ Simplify and solve for $x$ $-5x-2x + 12 = 5$ $-7x+12 = 5$ $-7x+12{-12} = 5{-12}$ $-7x = -7$ $\dfrac{-7x}{{-7}} = \dfrac{-7}{{-7}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = x-6}\thinspace$ to find $y$ ${y = }{(1)}{ - 6}$ $y = -5$ You can also plug ${x = 1}$ into $\thinspace {-5x-2y = 5}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - 2y = 5}$ ${y = -5}$